Question 1128046
Let {{{ x }}} = sum of husband and wife's ages
Let {{{ y }}} = sum of their children's ages
Let {{{ n }}} = the number of children
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(1) {{{ x = 4y }}}
(2) {{{ ( x - 8 ) / ( y - 4n ) = 18/1 }}}
(3) {{{ ( x + 4 ) / ( y + 2n ) = 3/1 }}}
( note that each parent and each child's age get
added to by number of years in future. The
opposite is true going into past )
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(2) {{{ x - 8 = 18*( y - 4n ) }}}
(2) {{{ x - 8 = 18y - 72n }}}
(2) {{{ x - 18y = 8 - 72n }}}
Plug (1) into (2)
(2) {{{ 4y - 18y = 8 - 72n }}}
(2) {{{ -14y = -72n +8 }}}
(2) {{{ 7y = 36n - 4 }}}
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(3) {{{ x + 4 = 3*( y + 2n ) }}}
(3) {{{ x + 4 = 3y + 6n }}}
(3) {{{ x - 3y = 6n - 4 }}}
(3) {{{ 4y - 3y = 6n - 4 }}}
(3) {{{ y = 6n - 4 }}}
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Multiply both sides of (3) by {{{ 6 }}}
and subtract (3) from (2)
(2) {{{ 7y = 36n - 4 }}}
(3) {{{ -6y = -36n + 24 }}}
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{{{ y = 20 }}}
and
{{{ x = 4y }}}
{{{ x = 80 }}}
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(3) {{{ ( x + 4 ) / ( y + 2n ) = 3/1 }}}
(3) {{{ ( 80 + 4 ) / ( 20 + 2n ) = 3/1 }}}
(3) {{{ 84 = 3*( 20 + 2n ) }}}
(3) {{{ 84 = 60 + 6n }}}
(3) {{{ 6n = 24 }}}
(3) {{{ n = 4 }}}
They have 4 children
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check:
(2) {{{ ( x - 8 ) / ( y - 4n ) = 18/1 }}}
(2) {{{ ( 80 - 8 ) / ( 20 - 4n ) = 18 }}}
(2) {{{ 72 = 18*( 20 - 4n ) }}}
(2) {{{ 72 = 360 - 72n }}}
(2) {{{ 72n = 288 }}}
(2) {{{ n = 4 }}}
OK
Get a 2nd opinion if this is incorrect